How many Americans would eagerly go to war to defend France ?
Not many.
But we're contractually obligated to defend them through the NATO mutual defense pact.
Likewise we are contractually obligated to defend Taiwan.
I doubt there are many Americans who wanted the U.S. to intervene in Haiti, Bosnia, Kosovo, Libya, or South Korea.
But I'm glad we did the right thing in these places. The U.S. pressing to do the right thing kept many of these brushfires from burning down the forest.
Where without U.S. leadership, the rest of the world would have let it burn.
And as I said, it is in China's long-term interest to wait it out for a gradual/peaceful China-Taiwan political re-unification, and not attempt it militarily.
But again:
1) An independent Taiwan's very existence (the enduring legacy of Chiang Kai Shek) flies in the face of mainland/communist China. The old guard is burning for the opportunity to eliminate that.
2) a volatile political/economic situation in China could hasten a military solution, to rally popular support by stroking nationalist strings, which is what a Taiwan invasion would provide.